Showing papers in "Advances in Mathematical Physics in 2022"

The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

Abstract: This article considers the stochastic fractional Radhakrishnan-Kundu-Lakshmanan equation (SFRKLE), which is a higher order nonlinear Schrödinger equation with cubic nonlinear terms in Kerr law. To find novel elliptic, trigonometric, rational, and stochastic fractional solutions, the Jacobi elliptic function technique is applied. Due to the Radhakrishnan-Kundu-Lakshmanan equation’s importance in modeling the propagation of solitons along an optical fiber, the derived solutions are vital for characterizing a number of key physical processes. Additionally, to show the impact of multiplicative noise on these solutions, we employ MATLAB tools to present some of the collected solutions in 2D and 3D graphs. Finally, we demonstrate that multiplicative noise stabilizes the analytical solutions of SFRKLE at zero.

The Exact Solutions of the Conformable Time-Fractional Modified Nonlinear Schrödinger Equation by the Trial Equation Method and Modified Trial Equation Method

Abstract: Using the trial equation method (TEM) and modified trial equation method (MTEM), firstly, we find the analytical solutions of the conformable time-fractional modified nonlinear Schrödinger equation (CTFMNLSE), and finally, we present numerical results in tables and charts.

Computational Simulations; Abundant Optical Wave Solutions Atangana Conformable Fractional Nonlinear Schrödinger Equation

Abstract: This research paper explores the Atangana conformable nonlinear fractional Schrödinger equation’s optical soliton wave solutions through three recently introduced computational schemes. The simplest expanded equation, the generalized Kudryashov method, and the sech-tanh expansion approaches are used for describing the structure of optical solitons by nonlinear optical fibers with the modern fractional operator. Several formulas such as hyperbolic, trigonometric, logical, dim, light, moon-bright hybrid, singular, combined singular, and regular wave solutions have been created. The employed methods are effective and worthy of being tested. The features of the Hamiltonian process were used to analyze the stability properties of the solutions obtained.

Corrected Inertial Torques of Gyroscopic Effects

Abstract: The published manuscripts in the area of gyroscope theory were presented mainly by the simplified approaches in which mathematical models contain many uncertainties. New research in machine dynamics opened breakthrough directions in gyroscopic effects of rotating objects that give the correct solutions. The pioneering work meets many problems when solving the scientific innovations that are accompanied by successes and omissions. New mathematical models for the gyroscopic inertial torques were derived with incorrect processing of the integral equations that give distorted results. The gyroscopic devices in engineering manifest gyroscopic effects as the action of the inertial torques which computing is crucial for mathematical describing of their motions. The corrected mathematical processing of the equations for the inertial torques acting in a gyroscope is presented in this manuscript.

Human Position Detection Based on Depth Camera Image Information in Mechanical Safety

Abstract: The devices used for human position detection in mechanical safety mainly include safety light curtain, safety laser scanner, safety pad, and vision system. However, these devices may be bypassed when used, and human or equipment cannot be distinguished. To solve this problem, a depth camera is proposed as a human position detection device in mechanical safety. The process of human position detection based on depth camera image information is given; it mainly includes image information acquisition, human presence detection, and distance measurement. Meanwhile, a human position detection method based on Intel RealSense depth camera and MobileNet-SSD algorithm is proposed and applied to robot safety protection. The result shows that the image information collected by the depth camera can detect the human position in real time, which can replace the existing mechanical safety human position detection device. At the same time, the depth camera can detect only human but not mobile devices and realize the separation and early warning of people and mobile devices.

Coupled Fixed Point Theorem for the Generalized Langevin Equation with Four-Point and Strip Conditions

Abstract: By considering a metric space with partially ordered sets, we employ the coupled fixed point type to scrutinize the uniqueness theory for the Langevin equation that included two generalized orders. We analyze our problem with four-point and strip conditions. The description of the rigid plate bounded by a Newtonian fluid is provided as an application of our results. The exact solution of this problem and approximate solutions are compared.

Noninteger Derivative Order Analysis on Plane Wave Reflection from Electro-Magneto-Thermo-Microstretch Medium with a Gravity Field within the Three-Phase Lag Model

Abstract: The present research paper illustrates how noninteger derivative order analysis affects the reflection of partial thermal expansion waves under the generalized theory of plane harmonic wave reflection from a semivacuum elastic solid material with both gravity and magnetic field in the three-phase lag model (3PHL). The main goal for this study is investigating the fractional order impact and the applications related to the orders, especially in biology, medicine, and bioinformatics, besides the integer order considering an external effect, such as electromagnetic, gravity, and phase lags in a microstretch medium. The problem fractional form was formulated, and the boundary conditions were applied. The results were displayed graphically, considering the 3PHL model with magnetic field, gravity, and relaxation time. These findings were an explicit comparison of the effect of the plane wave reflection amplitude with integer derivative order analysis and noninteger derivative order analysis. The fractional order was compared to the correspondence integer order that indicated to the difference between them and agreement with the applications in biology, medicine, and other related topics. This phenomenon has more applications in relation to the biology and biomathematics problems.

Exact Solutions of the Nonlinear Space-Time Fractional Partial Differential Symmetric Regularized Long Wave (SRLW) Equation by Employing Two Methods

Abstract: In this article, with the aid of Maple software, the exact solutions to the space-time fractional symmetric regularized long wave (SRLW) equation are successfully examined by $\left(G^{\prime }/G^2\right)$ -expansion and extended complex methods. Consequently, three types of traveling wave solutions are found such as Weierstrass double periodic elliptic functions, simply periodic functions, and the rational function solutions. The obtained results will play an important role in understanding and studying SRLW equation. It is easy to see that the extended complex and $\left(G^{\prime }/G^2\right)$ -expansion methods are reliable and will be used extensively to seek exact solutions of any other fractional nonlinear partial differential equations (FNPDE).

Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials

Abstract: The goal of this paper is study the mixed integral equation with singular kernel in two-dimensional adding to the time in the Volterra integral term numerically. We established the problem from the plane strain problem for the bounded layer medium composed of different materials that contains a crack on one of the interface. Also, the existence of a unique solution of the equation proved. Therefore, a numerical method is used to translate our problem to a system of two-dimensional Fredholm integral equations (STDFIEs). Then, Toeplitz matrix (TMM) and the Nystrom product methods (NPM) are used to solve the STDFIEs with Cauchy kernel. Numerical examples are presented, and their results are compared with the analytical solution to demonstrate the validity and applicability of the methods. The codes were written in Maple.

Certain Concepts of Interval-Valued Intuitionistic Fuzzy Graphs with an Application

Abstract: Interval-valued intuitionistic fuzzy graph (IVIFG), belonging to the FGs family, has good capabilities when facing with problems that cannot be expressed by FGs. When an element membership is not clear, neutrality is a good option that can be well supported by an IVIFG. The previous definitions of limitations in edge irregular FG have led us to offer new definitions in IVIFGs. Hence, in this paper, some types of edge irregular interval-valued intuitionistic fuzzy graphs (EI-IVIFGs) such as neighborly edge totally irregular (NETI), strongly edge irregular (SEI), and strongly edge totally irregular (SETI) are introduced. A comparative study between NEI-IVIFGs and NETI-IVIFGs is done. With the help of IVIFGs, the most efficient person in an organization can be identified according to the important factors that can be useful for an institution. Finally, an application of IVIFG has been introduced.

A New Bivariate Extended Generalized Inverted Kumaraswamy Weibull Distribution

Abstract: This article presents a new bivariate extended generalized inverted Kumaraswamy Weibull (BIEGIKw-Weibull) distribution with nine parameters. Statistical properties of the new distribution are discussed. Forms of copulas, moments, conditional moments, bivariate reliability function, and bivariate hazard rate function are derived. Maximum likelihood estimators are formulated. Simulation is conducted for three different sets of parameters to verify the theoretical results and to discuss the new distribution properties. The performance of the maximum likelihood method is investigated via Monte Carlo simulation depending on the bias and the standard error. Simulated lifetime data is used as an application of the new model.

Double Sumudu Transform Iterative Method for One-Dimensional Nonlinear Coupled Sine-Gordon Equation

Abstract: In this paper, the combined double Sumudu transform with iterative method is successfully implemented to obtain the approximate analytical solution of the one-dimensional coupled nonlinear sine-Gordon equation (NLSGE) subject to the appropriate initial and boundary conditions which cannot be solved by applying double Sumudu transform only. The solution of the nonlinear part of this equation was solved by a successive iterative method, the proposed technique has the advantage of producing an exact solution, and it is easily applied to the given problems analytically. Two test problems from mathematical physics were taken to show the liability, accuracy, convergence, and efficiency of the proposed method. Furthermore, the results indicate that the introduced method is promising for solving other types of systems of NLPDEs.

Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method

Abstract: The conformable fractional triple Laplace transform approach, in conjunction with the new Iterative method, is used to examine the exact analytical solutions of the (2 + 1)-dimensional nonlinear conformable fractional Telegraph equation. All the fractional derivatives are in a conformable sense. Some basic properties and theorems for conformable triple Laplace transform are presented and proved. The linear part of the considered problem is solved using the conformable fractional triple Laplace transform method, while the noise terms of the nonlinear part of the equation are removed using the novel Iterative method’s consecutive iteration procedure, and a single iteration yields the exact solution. As a result, the proposed method has the benefit of giving an exact solution that can be applied analytically to the presented issues. To confirm the performance, correctness, and efficiency of the provided technique, two test modeling problems from mathematical physics, nonlinear conformable fractional Telegraph equations, are used. According to the findings, the proposed method is being used to solve additional forms of nonlinear fractional partial differential equation systems. Moreover, the conformable fractional triple Laplace transform iterative method has a small computational size as compared to other methods.

Initial Value Problems with Generalized Fractional Derivatives and Their Solutions via Generalized Laplace Decomposition Method

Abstract: In this article, we use the p -Laplace decomposition method to find the solution to the initial value problems that involve generalized fractional derivatives. The p -Laplace decomposition method is used to get approximate series solutions. The Adomian decomposition is improved with the assistance of the p -Laplace transform to examine the solutions of the given examples to demonstrate the precision of the current technique.

∗ -Ricci Tensor on α -Cosymplectic Manifolds

Abstract: In this paper, we study α-cosymplectic manifold $M$ admitting $\ast$ -Ricci tensor. First, it is shown that a $\ast$ -Ricci semisymmetric manifold $M$ is $\ast$ -Ricci flat and a $\varphi$ -conformally flat manifold $M$ is an $\eta$ -Einstein manifold. Furthermore, the $\ast$ -Weyl curvature tensor ${\mathcal{W}}^{\ast }$ on $M$ has been considered. Particularly, we show that a manifold $M$ with vanishing $\ast$ -Weyl curvature tensor is a weak $\varphi$ -Einstein and a manifold $M$ fulfilling the condition $R\left(E_1,E_2\right)\cdot {\mathcal{W}}^{\ast }=0$ is $\eta$ -Einstein manifold. Finally, we give a characterization for α-cosymplectic manifold $M$ admitting $\ast$ -Ricci soliton given as to be nearly quasi-Einstein. Also, some consequences for three-dimensional cosymplectic manifolds admitting $\ast$ -Ricci soliton and almost $\ast$ -Ricci soliton are drawn.

Single and Multivalued Maps on Parametric Metric Spaces Endowed with an Equivalence Relation

Abstract: This article presents the E -parametric metric space, which is a generalized concept of parametric metric space. After that, the discussion is concerned with the existence of fixed points of single and multivalued maps on E -parametric metric spaces satisfying some contractive inequalities defined by an auxiliary function.

Using Image Feature Extraction to Identification of Ancient Ceramics Based on Partial Differential Equation

Abstract: This paper presents an in-depth study and analysis of the image feature extraction technique for ancient ceramic identification using an algorithm of partial differential equations. Image features of ancient ceramics are closely related to specific raw material selection and process technology, and complete acquisition of image features of ancient ceramics is a prerequisite for achieving image feature identification of ancient ceramics, since the quality of extracted area-grown ancient ceramic image feature extraction method is closely related to the background pixels and does not have generalizability. In this paper, we propose a deep learning-based extraction method, using Eased as a deep learning support platform, to extract and validate 5834 images of 272 types of ancient ceramics from kilns, celadon, and Yue kilns after manual labelling and training learning, and the results show that the average complete extraction rate is higher than 99%. The implementation of the deep learning method is summarized and compared with the traditional region growth extraction method, and the results show that the method is robust with the increase of the learning amount and has generalizability, which is a new method to effectively achieve the complete image feature extraction of ancient ceramics. The main content of the finite difference method is to use the ratio of the difference between the function values of two adjacent points and the distance between the two points to approximate the partial derivative of the function with respect to the variable. This idea was used to turn the problem of division into a problem of difference. Recognition of ancient ceramic image features was realized based on the extraction of the overall image features of ancient ceramics, the extraction and recognition of vessel type features, the quantitative recognition of multidimensional feature fusion ornamentation image features, and the implementation of deep learning based on inscription model recognition image feature classification recognition method; three-layer B/S architecture web application system and cross-platform system language called as the architectural support; and database services, deep learning packaging, and digital image processing. The specific implementation method is based on database service, deep learning encapsulation, digital image processing, and third-party invocation, and the service layer fusion and relearning mechanism is proposed to achieve the preliminary intelligent recognition system of ancient ceramic vessel type and ornament image features. The results of the validation test meet the expectation and verify the effectiveness of the ancient ceramic vessel type and ornament image feature recognition system.

A Parametric Analysis of the Effect of Hybrid Nanoparticles on the Flow Field and Homogeneous-Heterogeneous Reaction between Squeezing Plates

Abstract: Different strategies have been utilized by investigators with the intention of upgrading the thermal characteristics of ordinary liquids like water and kerosene oil. The focus is currently on hybrid nanomaterials since they are more efficient than nanofluids, so as to increase the thermal conductivity of fluids and mixtures. In a similar manner, this investigation is performed with the aim of breaking down the consistent mixed convection flow close to a two-dimensional unstable flow between two squeezing plates with homogeneous and heterogeneous reaction in the presence of hybrid nanoparticles of the porous medium. A sustainable suspension in the ethylene glycol with water is set by dissolving inorganic substances, iron oxide $\left({\text{Fe}}_3{\text{O}}_4\right)$ and cobalt (Co), to form ${\text{Fe}}_3{\text{O}}_4-\text{Co}/{\text{C}}_2{\text{H}}_6{\text{O}}_2-{\text{H}}_2\text{O}$ hybrid nanofluid. The numerical and analytical model portraying the fluid flow has been planned, and similitude conditions have been determined with the assistance of the same transformations. The shooting technique has been used to solve nonlinear numerical solution. To check the validity of the results obtained from the shooting mode, the Matlab built-in function BVP4c and Mathematica built-in function homotopy analysis method (HAM) are used. The influence of rising parameters on velocity, temperature, skin friction factor, Nusselt number, and Sherwood number is evaluated with the help of graphs and tables. It has been found in this work that to acquire a productive thermal framework, the hybrid nanoparticles should be considered instead of a single sort of nanoparticles. In addition, the velocities of both the hybrid nanofluids and simple nanofluids are upgraded by the mixed convection boundary, whereas they are decreased by the porosity. An augmentation in volumetric fraction of nanoparticles correlates to an increment in the heat transmission rate. It is also found that heat transfer rate for ${\text{Fe}}_3{\text{O}}_4-\text{Co}/{\text{C}}_2{\text{H}}_6{\text{O}}_2-{\text{H}}_2\text{O}$ hybrid nanofluids (HNF) is better than that of the ${\text{Fe}}_3{\text{O}}_4-{\text{C}}_2{\text{H}}_6{\text{O}}_2-{\text{H}}_2\text{O}$ of single nanofluids (SNF). This research shows that hybrid nanofluids play a significant part in the transfer of heat and in the distribution of nanofluids at higher temperatures.

Mathematical Physics Modelling and Prediction of Oil Spill Trajectory for a Catenary Anchor Leg Mooring (CALM) System

Abstract: The catenary anchor leg mooring (CALM) system usually moored a heavy oil tanker; due to its complex working mechanism and special working environment, oil spill accidents are easy to happen. Once the oil spill accident happens, it not only causes huge economic loss, but also kills the marine ecological environment. Oil spill trajectory model considers almost all weathering processes including evaporation, emulsification, dispersion, dissolution, photooxidation, sedimentation, and biodegradation. Model simulations indicated that both tidal currents and wind drag force have significant effect in oil spill movement. The dominant wind in the area is South-westerly wind during the summer monsoon and North-easterly wind during the winter monsoon, but South-westerly wind is far stronger and last longer than the North-easterly wind. As a result, oil spill trajectory is most likely towards offshore to North-east during the summer period (April to September). During the winter period (November–January), oil spill would move towards shore under North-westerly winds. Once oil reaches shore, it would stay at shore permanently and eventually sink to seabed or beach in the simulation. Although the model does not consider longshore drift by waves, oil movement along shore by waves would be a slow process. Therefore, the impact of oil spill during the winter monsoon would be limited to local area around Ras Markaz.

A Numerical and Analytical Study of a Stochastic Epidemic SIR Model in the Light of White Noise

Abstract: This study examines a novel SIR epidemic model that takes into account the impact of environmental white noise. According to the study, white noise has a significant impact on the disease. First, we establish the solution’s existence and uniqueness. Following that, we explain that the stochastic basic production R 0 is a threshold that determines the extinction or persistence of the disease. When noise levels are high, we acquire R 0 < 1 , which causes the sickness to disappear. A sufficient condition for the existence of a stationary distribution is archived when the noise intensity is high, which suggests the infection is prevalent when R 0 > 1 . Finally, numerical simulations are used to explain the key findings.

<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>M</mi> </math>-Lump Solution, Semirational Solution, and Self-Consistent Source Extension of a Novel <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mfenced open="(" c

Abstract: In this paper, we derive the M -lump solution in terms of Matsuno determinant for the combined KP3 and KP4 (cKP3-4) equation by applying the double-sum identities for determinant and investigate the dynamical behaviors of 1- and 2-lump solutions. In addition, we derive the Grammian solution for the cKP3-4 equation and construct the semirational solutions from the Grammian solution. Through the asymptotic analysis, we show that the semirational solutions describe fusion and fission of lumps and line solitons and rogue lump phenomena. Furthermore, we construct the cKP3-4 equation with self-consistent sources via the source generation procedure and present its Grammian and Wronskian solution.

An Improved Version of Residual Power Series Method for Space-Time Fractional Problems

Abstract: The task of present research is to establish an enhanced version of residual power series (RPS) technique for the approximate solutions of linear and nonlinear space-time fractional problems with Dirichlet boundary conditions by introducing new parameter $\lambda$ . The parameter $\lambda$ allows us to establish the best numerical solutions for space-time fractional differential equations (STFDE). Since each problem has different Dirichlet boundary conditions, the best choice of the parameter $\lambda$ depends on the problem. This is the major contribution of this research. The illustrated examples also show that the best approximate solutions of various problems are constructed for distinct values of parameter $\lambda$ . Moreover, the efficiency and reliability of this technique are verified by the numerical examples.

Sub-Lorentzian Geometry of Curves and Surfaces in a Lorentzian Lie Group

Abstract: We consider the sub-Lorentzian geometry of curves and surfaces in the Lie group $E\left(1,1\right).$ Firstly, as an application of Riemannian approximants scheme, we give the definition of Lorentzian approximants scheme for $E\left(1,1\right)$ which is a sequence of Lorentzian manifolds denoted by $E_{{\lambda }_1,{\lambda }_2}^L$ . By using the Koszul formula, we calculate the expressions of Levi-Civita connection and curvature tensor in the Lorentzian approximants of $E_{{\lambda }_1,{\lambda }_2}^L$ in terms of the basis $\left\{E_1,E_2,E_3\right\}.$ These expressions will be used to define the notions of the intrinsic curvature for curves, the intrinsic geodesic curvature of curves on surfaces, and the intrinsic Gaussian curvature of surfaces away from characteristic points. Furthermore, we derive the expressions of those curvatures and prove two generalized Gauss-Bonnet theorems in $E_{{\lambda }_1,{\lambda }_2}^L$ .

A Novel Description of Some Concepts in Interval-Valued Intuitionistic Fuzzy Graph with an Application

Abstract: Covering, matching, and domination are the basic concepts in graphs that play a decisive role in the properties of graphs. Calculating these parameters is one of the difficulties in fuzzy graphs when it is not possible to accurately determine the values of the vertices of a graph. The interval-valued intuitionistic fuzzy graph (IVIFG) is one of the fuzzy graphs which can play an important role in solving uncertain problems in different sciences such as psychology, biological sciences, medicine, and social networks. The necessity of using a range of value instead of one number caused them to help researchers in optimizing and saving time and cost. In this study, we introduce some of the specific concepts such as covering, matching, and paired domination using strong arc or effective edges by giving appropriate examples. In addition, we have calculated strong node covering number, strong independent number, and other parameters of complete bipartite IVIFGs with several examples. Finally, we have presented an application of IVIFG in social networks.

Multifeature Contrast Enhancement Algorithm for Digital Media Images Based on the Diffusion Equation

Abstract: This paper studies the processing of digital media images using a diffusion equation to increase the contrast of the image by stretching or extending the distribution of luminance data of the image to obtain clearer information of digital media images. In this paper, the image enhancement algorithm of nonlinear diffusion filtering is used to add a velocity term to the diffusion function using a coupled denoising model, which makes the diffusion of the original model smooth, and the interferogram is solved numerically with the help of numerical simulation to verify the denoising processing effect before and after the model correction. To meet the real-time applications in the field of video surveillance, this paper focuses on the optimization of the algorithm program, including software pipeline optimization, operation unit balancing, single instruction multiple data optimization, arithmetic operation optimization, and onchip storage optimization. These optimizations enable the nonlinear diffusion filter-based image enhancement algorithm to achieve high processing efficiency on the C674xDSP, with a processing speed of 25 posts per second for 640 × 480 size video images. Finally, the significance means a value of super pixel blocks is calculated in superpixel units, and the image is segmented into objects and backgrounds by combining with the Otsu threshold segmentation algorithm to mention the image. In this paper, the proposed algorithm experiments with several sets of Kor Kor resolution remote sensing images, respectively, and the Markov random field model and fully convolutional network (FCN) algorithm are used as the comparison algorithm. By comparing the experimental results qualitatively and quantitatively, it is shown that the algorithm in this paper has an obvious practical effect on contrast enhancement of digital media images and has certain practicality and superiority.

New Optical Solitons in Bragg Grating Fibers for the Nonlinear Coupled (<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mn>2</mn> <mo>+</mo> <mn>1</mn> </math>)-Dimensional Kundu-Mukherjee-Naskar System via Complete Discrimination System Method

Abstract: In this paper, the coupled Kundu-Mukherjee-Naskar (KMN) model in Bragg grating fibers is considered to retrieve some new optical soliton solutions in ( $2+1$ ) dimensions. Plenty of new exact solutions, including rational function solutions and triangle function solutions, in addition to the Jacobian elliptic function solutions, are obtained by using a complete discrimination system method. The 3D-surface plots, 2D-shape plots, and corresponding 2D contour plots of some obtained solutions are drawn, which provides a visualized structures and propagation of solitons. The novel results are new and show the effectiveness of the proposed method.

Generalization Contractive Mappings on Rectangular <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>b</mi> </math>-Metric Space

Abstract: In this paper, we introduce new coincidence fixed point theorems for generalized ϕ , ψ -contractive mappings fulfilling kind of an admissibility provision in a Hausdorff b -rectangular metric space with the support of C-functions. We applied our results to establish the existence of a solution for some integralitions. Finally, an example is presented to clarify our theorem.

Analytical Solution of One-Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method

Abstract: In this paper, the reduced differential transform method (RDTM) is successfully implemented to obtain the analytical solution of the space-time conformable fractional telegraph equation subject to the appropriate initial conditions. The fractional-order derivative will be in the conformable (CFD) sense. Some properties which help us to solve the governing problem using the suggested approach are proven. The proposed method yields an approximate solution in the form of an infinite series that converges to a closed-form solution, which is in many cases the exact solution. This method has the advantage of producing an analytical solution by only using the appropriate initial conditions without requiring any discretization, transformation, or restrictive assumptions. Four test modeling problems from mathematical physics, conformable fractional telegraph equations in which we already knew their exact solution using other numerical methods, were taken to show the liability, accuracy, convergence, and efficiency of the proposed method, and the solution behavior of each illustrative example is presented using tabulated numerical values and two- and three-dimensional graphs. The results show that the RDTM gave solutions that coincide with the exact solutions and the numerical solutions that are available in the literature. Also, the obtained results reveal that the introduced method is easily applicable and it saves a lot of computational work in solving conformable fractional telegraph equations, and it may also find wide application in other complicated fractional partial differential equations that originate in the areas of engineering and science.

Research on Fuzzy Decision-Making Method of Task Allocation for Ship Multiagent Collaborative Design

Abstract: Since task allocation is one of the core tasks of ship design, the choice of its allocation strategy is a key factor that affects whether the task and the design agent can be beneficially matched. Different from the traditional one-way assignment mode of assigning tasks to designers, in the task assignment strategy of modern ship collaborative design mode, designers’ ability and benefit ratio is getting higher and higher. Therefore, in order to improve the efficiency and quality of task design, this paper proposes a multidesign agent-task allocation decision-making method. In this paper, the task attributes and designers’ attributes are introduced into the task allocation strategy model, and the fuzzy linguistic variable method is used to build the evaluation index matrix of the design agent, and the task timeliness function is established. Secondly, the multidesign agent-task benefit function is established and solved to obtain the best allocation strategy. Finally, through example verification and comparative analysis with the Round-Robin algorithm (RR) and the Weighted Round-Robin (WRR) algorithm, the validity, feasibility, and stability of the multidesign agent-task allocation decision-making method proposed in this paper are verified, and it is proved that the task allocation method takes the bilateral needs of the task and the design agent into account, solves the optimal allocation strategy of collaborative design tasks, and realizes the balanced allocation between the ship collaborative design task and the design agent.

An Analytical and a Numerical Method for Nonlinear Convection-Radiation Problems in Porous Fins

Abstract: The present work shows an analytical and a numerical method for heat transfer nonlinear problems in porous fins using the Darcy model. Numerical simulations are carried out with the aid of a sequence of linear problems, each of them possessing an equivalent minimum principle, that has as its limit the solution of the original problem. The nonlinear convection-radiation heat transfer process is considered and simulated by means of a finite difference scheme. Results showed the relevance of the radiation for realistic thermal mapping in porous media with percentage errors of up to 40% for the last nodes.